The club has announced two friendly matches in the war-torn south-east Asian country formerly known as Burma, but has faced criticism from fans online.
Labour MP for Bassetlaw John Mann, a vocal Leeds supporter, told The Yorkshire Post: "They should be sorting out new signings rather than flying to conflict zones and assisting a brutal regime".
Liberal Democrat leader in the House of Lords, Lord Newby, who is also a Leeds fan, said: "I'm appalled that Leeds United are giving the regime in Burma credibility by visiting the country."
Leeds United denied supporting the Myanmar regime, saying it was working with the Football League in the country and the AYA Bank in arranging the games.
Myanmar has been the scene of severe political unrest in the past 12 months with its regime accused of ethnically cleansing Rohingya Muslims, who are not given citizenship or legal status in the country and have faced persecution for years.
In February, Foreign Secretary Boris Johnson accused Myanmar of "industrial ethnic cleansing" of Rohingya Muslims in northern Rakhine province.
He told ITV News: "There is no doubt when you fly over northern Rakhine and you look at the scale of the devastation, the industrial ethnic cleansing that has gone on, there is no doubt that the military must have been involved."
In March, the United Nations said there is "no other conclusion" to be reached from visiting the Cox's Bazar refugee camp in Bangladesh, which has taken in hundreds of thousands of Rohingya people, that ethnic cleansing was continuing.
Aung Sang Suu Kyi, the de facto leader of Myanmar, was in November formally stripped of an honour granting her the Freedom of Oxford due to her response to the Rohingya crisis.
Leeds United said they were "delighted" to announce the tour, which will see the club play friendlies against Myanmar National League All Stars in Yangon on May 9, and the national team in Mandalay on May 11.
Responding to Mr Mann's comments, a Leeds United spokesman said: "Leeds United are not supporting any regime or government.
"We have worked with the Football League in Myanmar as well as the AYA Bank in making the arrangements for the games.
"We firmly believe that football brings people together and we aim to engage millions of young football supporters and thousands of players who share a love of the game."
Managing director Angus Kinnear said: "Myanmar is one of the fastest growing nations in South East Asia and is passionate about English football. They have ambitious goals for grassroots and elite football development that we are delighted to be able to support. This tour gives us an opportunity to meet new fans of football who will hopefully support our journey back to the Premier League in the coming years."
“From a football perspective we welcome the opportunity for our players who have not featured much in the past six months due to injuries the chance to continue their rehabilitation. The squad are very excited for the chance to represent the club in Asia.”
General secretary of the Myanmar Football Federation U Ko Ko Thein said: "We are very pleased to welcome an English club with the history and heritage of Leeds United. The football infrastructure in Myanmar continues to improve and develop, and this is an important milestone on our journey"
"Myanmar is a football-mad country and this tour will help us to showcase our passion for the game at and abroad. I'd like to thank the sponsors of the tour AYA Bank, and of course Leeds United for coming to play here. We wish them very well for the future."